A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 



If we determine x from the equation 



581 



dz' 

 and F', G', H' from the equations 



F' = F_dx Q' = Q^^K H' = H-^ (74) 



dx ' dy' dz" 



then 



dx dy dz 

 and the equations in (94) become of the form 



Differentiating the three equations with respect to x, y, and z, and adding, we 

 find that 



d x 



dt ' '\''/> 



and that kV*F' = 4irp. ^- 



(78). 



Hence the disturbances indicated by F', G', H' are propagated with the velocity 



F= /- - through the field; and since 



dF' dG' dH' 



-T- + -5-+-5 = 0, 

 dx dy dz 



the resultant of these disturbances is in the plane of the wave. 



(99) The remaining part of the total disturbances F, G, II being the part 

 depending on ^, is subject to no condition except that expressed in the equation 



_ 

 dt * dt>~ 



